The　multi-criteria　degree-constrained　minimum　spanning　tree　problem　(mcd-MST)　is　an　important　issue　in　wireless　sensor　networks　(WSNs)　topology　control.　However,　the　multi-criteria　MST　(mc-MST)　is　NP-hard　problem　and　mcd-MST　is　a　typical　mc-MST.　In　this　paper,　we　present　an　improved　discrete　particle　swarm　optimization　(PSO)　approach　for　mcd-MST　which　gives　a　good　compromise　between　many　key　objectives　in　WSNs　such　as　energy　consumption,　reliability,　QoS　provisioning　and　so　on.　The　principles　of　mutation　and　crossover　operator　in　the　genetic　algorithm　(GA)　are　incorporated　into　the　proposed　PSO　algorithm　to　achieve　a　better　diversity　and　break　away　from　local　optima.　The　proposed　algorithm　is　compared　with　an　enumeration　method.　The　simulation　results　show　that　this　algorithm　is　efficient　and　finds　high　quality　solutions　for　mcd-MST.　©　2009　IEEE.